Why do we round five up when it’s exactly in the middle?
In: Mathematics
Because we had to pick one or the other, and 5 rounding up meant that five digits rounded up (5,6,7,8,9) and five rounded down (0,1,2,3,4). Rounding is not a mathematical law, it’s just how we choose to do things.
it was just chosen as the standard. Nothing mathematically important about it – it’s just a good idea that when you use a term like ’round the number’, there everyone is on the same page
Not everyone does, some fields prefer to “round to even” to reduce bias. In this rounding, you round a 5 up or down so that the new final digit is even.
Well when rounding to the nearest tens place 5 is right in the middle so if we wanted to round it we could go up or down equally. We chose to go up because that was just the convention we chose, no other reason than that. They might have had their reasons why they liked that way better but mathmatically it was just what they decided to go with. Rounding is a man made concept so this was one of the rules we all agreed upon when agreeing on how we will round numbers.
There is also a less common “round half to even” convention used in some fields (e.g. finance, accounting, certain branches of science and engineering), for bias reduction. For example, 1.5 rounds to 2, and 2.5 also rounds to 2. This distributes rounding errors more evenly over a dataset, reducing the likelihood of cumulative error.
If it’s exactly 5, it’s just as far from 0 as 10. But if you have 5.something it will be closer to 10, so if you always round up you will be right without having to worry if there are decimals behind the 5 or not.
There’s nothing in math to actually say that exactly 5 should be rounded one way or another. It’s exactly halfway between 0 and 10.
But one big thing is that you would round 5.00000000000000000000000000000000000000000001 up, and it would feel very wrong to round that up but not exactly 5. If you rounded 5 down, you would only round *exactly* 5 and not 5 + some very small amount, which can be more weird.
In technical scientific papers, numbers ending in a five *and any non—zero digit after* get rounded up because non—zero digits increase the value of the number and bring it closer to the next higher number.
However, if there is a number to be rounded which ends in a five *and does not have any further non—zero digits*, a tie—breaking rule is applied to avoid skewing any mathematical calculations with the data.
One common example of this is a rule called “***round half to even***”. Under this, 3.350 rounds to 3.4, but 3.250 rounds to 3.2. This ensures that rounding does not bias the data.
If a value is reported or measured to be 0.500000000000 we would be pretty confident of saying is it pretty much exactly in the middle between 0 and 1.
But if that value is reported or measured to be 0.5, there’s a very high likelihood that we are missing some significant digits after the 5 that would make the value closer to 1 than to 0.
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